Write MapReduce algorithms for computing the following operations on bags R and S: (a) Bag Union, defined to be the bag of tuples in which tuple t appears the sum of the numbers of times it appears in R and S. (b) Bag Intersection, defined to be the bag of tuples in which tuple t appears the minimum of the numbers of times it appears in R and S. (c) Bag Difference, defined to be the bag of tuples in which the number of times a tuple t appears is equal to the number of times it appears in R minus the number of times it appears in S. A tuple that appears more times in S than in R does not appear in the difference.